What is the value of sin(arcsin(1)+arccos(1/2)) ?

The value of sin(arcsin(1)+arccos(1/2)) is 1/2

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sin(arcsin(1)+arccos(1/2))

sin (arcsin (1) + arccos (\frac{1}{2}))

\frac{1}{2}

Decimal Notation

0.5

Solution steps

sin (arcsin (1) + arccos (\frac{1}{2}))

Rewrite using trig identities:

sin (arcsin (1)) cos (arccos (\frac{1}{2})) + cos (arcsin (1)) sin (arccos (\frac{1}{2}))

sin (arcsin (1) + arccos (\frac{1}{2}))

Use the Angle Sum identity:

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

= sin (arcsin (1)) cos (arccos (\frac{1}{2})) + cos (arcsin (1)) sin (arccos (\frac{1}{2}))

= sin (arcsin (1)) cos (arccos (\frac{1}{2})) + cos (arcsin (1)) sin (arccos (\frac{1}{2}))

Rewrite using trig identities:

sin (arcsin (1)) = 1

Use the following identity:

sin (arcsin (x)) = x

= 1

Rewrite using trig identities:

cos (arccos (\frac{1}{2})) = \frac{1}{2}

Use the following identity:

cos (arccos (x)) = x

= \frac{1}{2}

Rewrite using trig identities:

cos (arcsin (1)) = 0

cos (arcsin (1))

Rewrite using trig identities:

cos (arcsin (1)) = 1 - 1^{2}

Use the following identity:

cos (arcsin (x)) = 1 - x^{2}

= 1 - 1^{2}

= 1 - 1^{2}

Simplify

= 0

Rewrite using trig identities:

sin (arccos (\frac{1}{2})) = \frac{3}{2}

sin (arccos (\frac{1}{2}))

Rewrite using trig identities:

sin (arccos (\frac{1}{2})) = 1 - (\frac{1}{2})^{2}

Use the following identity:

sin (arccos (x)) = 1 - x^{2}

= 1 - (\frac{1}{2})^{2}

= 1 - (\frac{1}{2})^{2}

Simplify

= \frac{3}{2}

= 1 \cdot \frac{1}{2} + 0 \cdot \frac{3}{2}

Simplify

= \frac{1}{2}

csc (\frac{3}{4})

arctan (- \frac{5}{8})

10 cos (π)

arccos (cos (2))

\frac{cos ( 7 π )}{12}

What is the value of sin(arcsin(1)+arccos(1/2)) ?
The value of sin(arcsin(1)+arccos(1/2)) is 1/2